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SSC CHSL 7 Jan 2017 Shift 1 Paper

Question : 64 of 100

Marks: +1, -0

If cosC - cosD = x, then value of x is

Solution:

We know that, cos (x+y) = cosx cosy - sinx siny ----(i)

and cos (x-y) = cosx cosy + sinx siny -----(ii)

Subtracting equations (ii) from (i), we get :

cos (x+y) - cos (x-y) = - 2 sinx siny ----------(iii)

Let x+y = C and x-y = D

⇒

x=\frac{C+D}{2}

⇒ and

y=\frac{C-D}{2}

Substituting above values in equation (iii)

⇒

\cos C - \cos D

= -2\sin\left(\frac{C+D}{2}\right)\sin\left(\frac{C-D}{2}\right)

⇒

\cos C - \cos D

= 2\sin\left(\frac{C+D}{2}\right)\sin\left(\frac{D-C}{2}\right)

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